Chris and Mike, (01)
CP
> examples below (FRN etc.) are more about modality than change - a
> common approach is (as Matthew West has very recently noted) is
> possible worlds. (02)
MB
> From a separation of concerns perspective, it makes sense to distinguish
> between change over time and different possible futures (as we do with
> tense in English). (03)
I would just like to clarify some points: (04)
1. The term 'possible world' in Kripke semantics is not the same
as computational simulations of possible states of the world. (05)
2. A Kripke possible world is a member of an abstract set,
whose elements happen to be called worlds. The semantics
of modality is pushed into an *accessibility relation* R,
which states which worlds are accessible from which other
worlds. (06)
3. But computational systems are based on simulations of
possible worlds or theories about them. The notion of
accessibility is either absent or of minimal interest. (07)
For these reasons, it is more intuitively meaningful and
computationally more practical to use an alternative (but
logically equivalent) semantics specified by Michael Dunn: (08)
1. Each possible world is specified by a set of laws L
(which can be considered the axioms of an ontology
for that world) plus a set of facts about that world
(which can be considered the deductive closure of L
plus a database about everything in that world). (09)
2. Then Dunn showed that Kripke's accessibility relation
can be derived from the laws of the worlds: a world w2
is accessible from a world w1 iff all the laws of w1
remain true in w2, but some of them might be demoted
from the status of laws to just facts in w2. (010)
Dunn's semantics makes the definition of modality much
more intuitive and easier to implement than Kripke's: (011)
* A statement is necessary in world w iff it is provable
from the laws (ontology) of w. (012)
* A statement is possible in w iff it is consistent
with the laws (ontology) of w. (013)
Dunn's method can also be used for reasoning about the future,
either by proving theorems about how the facts will change under
the given ontology or by running a simulation program that is
based on the ontology. (014)
For more about Dunn's semantics, its relationship to Kripke's
semantics, and its use in ontology and computation, see (015)
http://www.jfsowa.com/pubs/laws.htm
Laws, Facts, and Contexts: Foundations for Multimodal Reasoning (016)
http://www.jfsowa.com/pubs/worlds.pdf
Worlds, Models, and Descriptions (017)
John (018)
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